A test of time dilation with an optical atomic clock on a stratospheric balloon

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The performance of state-of-the-art optical lattice clocks offers an opportunity for an improved test of one of the fundamental effects of General Relativity, the time dilation in the gravitational potential. The most precise test of this effect was performed 40 years ago by comparing two microwave clocks on a 10 000 km height difference. A new, non-satellite test of this effect with a competitive precision necessarily implies the need to operate an optical clock outside of the laboratory. Here we propose to build a ytterbium optical lattice clock and to use it as a probe clock on significant altitudes to precisely measure the gravitational time dilation through a frequency comparison with a reference clock on the ground. We aim at a precision of the measurement better than that of the upcoming space mission ACES (2017-18), which employs a cold-atom Cs microwave clock. To achieve the goals of the project, we propose to develop a flyable optical clock (FOC), a particularly compact and robust apparatus, which additionally comprises, for the first time, two atomics subsystems, allowing for in-depth characterization and optimization of performance towards our specific experiment. In order to relax the requirement of accuracy for both the probe and the reference clock, in our application we foresee that during each experiment they are first compared on ground, before the FOC is brought to altitude and the comparison is repeated. Thus, the main requirement is the reproducibility of the FOCs and the references frequency. Furthermore, achieving high frequency stability is crucial in order to minimize the integration time during the measurement campaign, whose duration is limited. In a 7-year long project, we plan to perform experiments of increasing complexity, concerning both the vertical distance and the link between the two clocks. In a demonstration experiment (year 4), the FOC will be operated in the panoramic level of the television tower in Düsseldorf, 160 m above the reference clock on ground, which is connected through a fiber link and intercompared. This will provide a test of the gravitational time dilation at the 1E-3 level. In the final part of the project (years 7), a mission will be performed in which the FOC will be operated on a stratospheric balloon at an altitude of 35 km for approximately 10 hours. The frequency link for comparison with the reference clock on ground will be a frequency-comb-based two-way free-space laser link, to be implemented in collaboration with colleagues from NIST and ViaLight in years 4-6. By averaging down the statistical uncertainty of the frequency difference of the FOC and reference clock to the 2E-18 level, we aim for a measurement of the gravitational time dilation with relative uncertainty of 5E-7, approximately a factor of 4 better than the expected goal of the ACES mission.